Answer:
Diameter of the pipe ≈ 6.77 ft
Step-by-step explanation:
Volume of a cylinder = πr²h
Here, r = Radius of the cylindrical pipe
h = Length of the pipe
Volume of the pipe = 900 ft³
Length of the pipe = 25 ft
By substituting the given values in the formula,
900 = π(r)²(25)
r² =
r = √11.459
r = 3.385
Diameter = 2(radius)
= 2(3.385)
= 6.77 ft
One way of solving this problem can be Heron's formula. It is a formula that allows us to compute the area of a triangle, knowing the length of its three sides.
For the sake of clarity, let's assume that the point in the top-left lies in the origin, and let's call it point A. Then, the "middle" point is point B, and the bottom-right point is point C.
If we fix the coordinate axis with the origin in A, we have the following coordinates for the three points:
We can compute the length of any side using the formula for the distance between two points:
Plugging the approriate values, we get the following lenghts:
Now that we have the lengths, we can use Heron's formula: given the side lenghts and the semiperimeter
, the area is given by
If you plug our values, you will get an area of 6.5. So, unless I'm mistaken, none of the answers seem to mach, whereas 7 seems the best approximation.